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Thermal Distribution in a Pack of Cylindrical Batteries
Introduction
This example demonstrates how to model the temperature distribution in a battery pack during a 4C discharge. The pack is constructed by first coupling two cylindrical batteries in parallel. Six parallel-connected pairs are then connected in series to create the full pack - a configuration also called 6s2p. This configuration for the lithium ion battery pack is quite common in portable devices like skateboards, toys, drones and medical equipments.The symmetry of the problem is used twice so that only the temperature distribution for three batteries needs to be solved for.
Three instances of the Lumped Battery interface are used to generate the appropriate heat sources, which are then coupled to one Heat Transfer interface in a 3D geometry.
For a detailed description of the Lumped Battery interface and the underlying model, see the Parameter Estimation of a Time-Dependent Lumped Battery Model tutorial.
Model Definition
Figure 1 shows the model geometry. Three 21,700 battery cylinders (21 mm in diameter, 70 mm high) are placed adjacent to each other. Small connecting strips of aluminum are located at the top and bottom of the cylinders according to the 6s2p configuration. The whole pack is assumed to be wrapped in plastic, forming a domain filled with air. Assuming a nominal capacity of 4 Ah for each cell and nominal voltage of 3.6 V, the battery pack has a total nominal capacity of approximately 177 Wh.
Figure 1: Model geometry.
One Lumped Battery interface is used to model each battery cylinder, with temperature-dependent ohmic, exchange current and diffusion time-constant parameters according to Arrhenius expressions.
The temperature profile is modeled using a Heat Transfer interface, where the heat sources stemming from the battery models are added by the use of an Electrochemical Heating multiphysics nodes. The convection in the air-filled domain enclosing the batteries is neglected, assuming quiescent conditions. The outer boundaries of the pack are cooled using a convective cooling condition. Symmetry (no flux) conditions are used for the interior flat symmetry boundaries facing the rest of the pack.
Anisotropic heat conductivities are used in each battery by the use of individually defined cylindrical coordinate systems for each battery cylinder, with generally lower heat conductivities in the radial direction compared to the angular and z directions - a result of the spirally wound metal foils in the jelly roll design of the batteries.
The pack is discharged from 100% to 20% state-of-charge (SOC) using a 4C rate for 12 minutes.
Results and Discussion
Figure 2 shows the temperature distribution in the pack at the end of the simulation, where the solution data has been mirrored twice to illustrate the temperature of the full 6s2p pack. The innermost parts of the pack experience a temperature about 2ºC higher than the outermost parts.
Figure 2: Temperature plot at t= 0.2 h.
Figure 3 shows a plot of the individual cell voltages during the discharge. The outermost cell (Cell 1) exhibits a slightly lower discharge voltage, a result of the ohmic drop and exchange current being slightly lower, and the diffusion time constant slightly higher, for the lower temperature, but the effect is small. The corresponding temperatures are shown in Figure 4.
Figure 3: Cell voltages versus time.
Figure 4: Average cell temperatures versus time.
Application Library path: Battery_Design_Module/Thermal_Management/lumped_li_battery_pack_6s2p
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, Start with adding a 3D space dimension along with a Heat Transfer in Fluids and a Lumped Battery interface.
2
click  3D.
3
In the Select Physics tree, select Heat Transfer>Heat Transfer in Fluids (ht).
4
Click Add.
5
In the Select Physics tree, select Electrochemistry>Batteries>Lumped Battery (lb).
6
Click Add.
7
Click  Study.
8
In the Select Study tree, select General Studies>Time Dependent.
9
Click  Done.
Definitions
Add an analytical function to account for the temperature dependent activation energy using the Arrhenius relation.
Analytic 1 (an1)
1
In the Home toolbar, click  Functions and choose Local>Analytic.
2
In the Settings window for Analytic, type Arrh in the Function name text field.
3
Locate the Definition section. In the Expression text field, type exp(Ea/R_const*(1/Temp-1/T0)).
4
In the Arguments text field, type Ea, Temp.
5
Locate the Units section. In the table, enter the following settings:
Argument
Unit
Ea
J/mol
Temp
K
6
In the Function text field, type 1.
E_OCP
Next add interpolation functions to define the SOC dependent equilibrium potential and its temperature dependence.
1
In the Home toolbar, click  Functions and choose Local>Interpolation.
2
In the Settings window for Interpolation, type E_OCP in the Label text field.
3
Locate the Definition section. From the Data source list, choose File.
4
In the Filename text field, type lumped_li_battery_pack_6s2p_E_OCP_data.txt.
5
Locate the Units section. In the Argument table, enter the following settings:
Argument
Unit
Column 1
1
6
In the Function table, enter the following settings:
Function
Unit
int1
V
dEdT
1
In the Home toolbar, click  Functions and choose Local>Interpolation.
2
In the Settings window for Interpolation, type dEdT in the Label text field.
3
Locate the Definition section. From the Data source list, choose File.
4
In the Filename text field, type lumped_li_battery_pack_6s2p_dEdT_data.txt.
5
Locate the Units section. In the Argument table, enter the following settings:
Argument
Unit
Column 1
1
6
In the Function table, enter the following settings:
Function
Unit
int2
V/K
Geometry 1
The model geometry is available as a parameterized geometry sequence in a separate MPH-file. If you want to build it from scratch, follow the instructions in the section Appendix — Geometry Modeling Instructions. Otherwise load it from file with the following steps.
1
In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
2
Browse to the model’s Application Libraries folder and double-click the file lumped_li_battery_pack_6s2p_geom_sequence.mph.
3
In the Geometry toolbar, click  Build All.
4
Click the  Transparency button in the Graphics toolbar.
5
Click the  Zoom Extents button in the Graphics toolbar.
Global Definitions
Geometry Parameters
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, type Geometry Parameters in the Label text field.
Battery Parameters
Add the parameter file required for setting up the physics of the lumped battery and heat transfer interfaces.
1
In the Home toolbar, click  Parameters and choose Add>Parameters.
2
In the Settings window for Parameters, type Battery Parameters in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file lumped_li_battery_pack_6s2p_parameters.txt.
Definitions
Add cylindrical coordinate systems to define the rotational symmetry around the batteries. This will be needed when setting material properties for the heat transfer interface.
Cylindrical System 2 (sys2)
In the Definitions toolbar, click  Coordinate Systems and choose Cylindrical System.
Cylindrical System 3 (sys3)
1
Right-click Cylindrical System 2 (sys2) and choose Duplicate.
2
In the Settings window for Cylindrical System, locate the Settings section.
3
Find the Origin subsection. In the table, enter the following settings:
x (m)
y (m)
z (m)
d_batt
0
0
Cylindrical System 4 (sys4)
1
Right-click Cylindrical System 3 (sys3) and choose Duplicate.
2
In the Settings window for Cylindrical System, locate the Settings section.
3
Find the Origin subsection. In the table, enter the following settings:
x (m)
y (m)
z (m)
2*d_batt
0
0
Materials
Next, add and define the materials in the different domains: air to the region surrounding the batteries and aluminum to the current collectors.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Air.
4
Click Add to Component in the window toolbar.
5
In the tree, select Built-in>Aluminum.
6
Click Add to Component in the window toolbar.
7
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Air (mat1)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Air (mat1).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Air Domain.
Aluminum (mat2)
1
In the Model Builder window, click Aluminum (mat2).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Connectors.
Active Battery Material
Add a blank material to define the thermal properties of the active battery material manually.
1
In the Model Builder window, right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Active Battery Material in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Batteries.
4
In the Model Builder window, expand the Component 1 (comp1)>Materials>Active Battery Material (mat3) node, then click Basic (def).
5
In the Settings window for Basic, locate the Output Properties section.
6
Click  Select Quantity.
7
In the Physical Quantity dialog box, select General>Density (kg/m^3) in the tree.
8
Click OK.
9
In the Settings window for Basic, locate the Output Properties section.
10
In the table, enter the following settings:
Property
Variable
Expression
Unit
Size
Density
rho
rho_batt
kg/m³
1x1
11
Click  Select Quantity.
12
In the Physical Quantity dialog box, select Transport>Heat capacity at constant pressure (J/(kg*K)) in the tree.
13
Click OK.
14
In the Settings window for Basic, locate the Output Properties section.
15
In the table, enter the following settings:
Property
Variable
Expression
Unit
Size
Heat capacity at constant pressure
Cp
Cp_batt
J/(kg·K)
1x1
Heat Transfer in Fluids (ht)
Now define the heat transfer in the battery pack.
Initial Values 1
1
In the Model Builder window, under Component 1 (comp1)>Heat Transfer in Fluids (ht) click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T text field, type T_init.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose Heat Flux Boundaries.
4
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
5
In the h text field, type ht.
6
In the Text text field, type T_init.
Solid 1
1
In the Physics toolbar, click  Domains and choose Solid.
2
In the Settings window for Solid, locate the Domain Selection section.
3
From the Selection list, choose Battery 1.
4
Locate the Coordinate System Selection section. From the Coordinate system list, choose Cylindrical System 2 (sys2).
5
Locate the Heat Conduction, Solid section. From the k list, choose User defined. From the list, choose Diagonal.
6
In the k table, enter the following settings:
kT_batt_r
0
0
0
kT_batt_ang
0
0
0
kT_batt_ang
Solid 2
1
Right-click Solid 1 and choose Duplicate.
2
In the Settings window for Solid, locate the Domain Selection section.
3
From the Selection list, choose Battery 2.
4
Locate the Coordinate System Selection section. From the Coordinate system list, choose Cylindrical System 3 (sys3).
Solid 3
1
In the Model Builder window, under Component 1 (comp1)>Heat Transfer in Fluids (ht) right-click Solid 1 and choose Duplicate.
2
In the Settings window for Solid, locate the Domain Selection section.
3
From the Selection list, choose Battery 3.
4
Locate the Coordinate System Selection section. From the Coordinate system list, choose Cylindrical System 4 (sys4).
Solid 4
1
In the Physics toolbar, click  Domains and choose Solid.
2
In the Settings window for Solid, locate the Domain Selection section.
3
From the Selection list, choose Connectors.
Lumped Battery (lb)
Now define the battery characteristics in the lumped battery interface.
1
In the Model Builder window, under Component 1 (comp1) click Lumped Battery (lb).
2
In the Settings window for Lumped Battery, locate the Domain Selection section.
3
From the Selection list, choose Battery 1.
4
Locate the Operation Mode section. In the Iapp text field, type -I_1C*C_rate.
5
Locate the Battery Settings section. In the Qcell,0 text field, type Q_cell.
6
In the SOCcell,0 text field, type 1.
Cell Equilibrium Potential 1
1
In the Model Builder window, under Component 1 (comp1)>Lumped Battery (lb) click Cell Equilibrium Potential 1.
2
In the Settings window for Cell Equilibrium Potential, locate the Open Circuit Voltage section.
3
From the Open circuit voltage input list, choose From definitions.
4
From the EOCV,ref list, choose E_OCP (int1).
5
From the dEOCV/dT list, choose dEdT (int2).
Voltage Losses 1
1
In the Model Builder window, click Voltage Losses 1.
2
In the Settings window for Voltage Losses, locate the Ohmic Overpotential section.
3
In the ηIR,1C text field, type eta_1C*Arrh(Ea_eta1C, lb.Temp).
4
Locate the Activation Overpotential section. In the J0 text field, type J0_0*Arrh(Ea_J0,lb.Temp).
5
Locate the Concentration Overpotential section. Select the Include concentration overpotential check box.
6
In the τ text field, type tau_0*Arrh(Ea_Tau,lb.Temp).
Copy the lumped battery interface node, and then modify the settings of the copy, to define the second battery in the pack.
7
In the Model Builder window, right-click Lumped Battery (lb) and choose Copy.
Lumped Battery 2 (lb2)
1
In the Model Builder window, right-click Component 1 (comp1) and choose Paste Lumped Battery.
2
In the Messages from Paste dialog box, click OK.
3
In the Settings window for Lumped Battery, locate the Domain Selection section.
4
From the Selection list, choose Battery 2.
Voltage Losses 1
1
In the Model Builder window, expand the Lumped Battery 2 (lb2) node, then click Voltage Losses 1.
2
In the Settings window for Voltage Losses, locate the Ohmic Overpotential section.
3
In the ηIR,1C text field, type eta_1C*Arrh(Ea_eta1C, lb2.Temp).
4
Locate the Activation Overpotential section. In the J0 text field, type J0_0*Arrh(Ea_J0,lb2.Temp).
5
Locate the Concentration Overpotential section. In the τ text field, type tau_0*Arrh(Ea_Tau,lb2.Temp).
Lumped Battery (lb)
In the Model Builder window, under Component 1 (comp1) right-click Lumped Battery (lb) and choose Copy.
Lumped Battery 3 (lb3)
1
In the Model Builder window, right-click Component 1 (comp1) and choose Paste Lumped Battery.
2
In the Messages from Paste dialog box, click OK.
3
In the Settings window for Lumped Battery, locate the Domain Selection section.
4
From the Selection list, choose Battery 3.
Voltage Losses 1
1
In the Model Builder window, expand the Lumped Battery 3 (lb3) node, then click Voltage Losses 1.
2
In the Settings window for Voltage Losses, locate the Ohmic Overpotential section.
3
In the ηIR,1C text field, type eta_1C*Arrh(Ea_eta1C, lb3.Temp).
4
Locate the Activation Overpotential section. In the J0 text field, type J0_0*Arrh(Ea_J0,lb3.Temp).
5
Locate the Concentration Overpotential section. In the τ text field, type tau_0*Arrh(Ea_Tau,lb3.Temp).
Multiphysics
Electrochemical Heating 1 (ech1)
In the Physics toolbar, click  Multiphysics Couplings and choose Domain>Electrochemical Heating.
Electrochemical Heating 2 (ech2)
1
In the Physics toolbar, click  Multiphysics Couplings and choose Domain>Electrochemical Heating.
2
In the Settings window for Electrochemical Heating, locate the Domain Selection section.
3
From the Selection list, choose Manual.
4
Locate the Coupled Interfaces section. From the Electrochemical list, choose Lumped Battery 2 (lb2).
Electrochemical Heating 3 (ech3)
1
Right-click Electrochemical Heating 2 (ech2) and choose Duplicate.
2
In the Settings window for Electrochemical Heating, locate the Coupled Interfaces section.
3
From the Electrochemical list, choose Lumped Battery 3 (lb3).
Definitions (comp1)
Adding probes for Temperature and Cell Potential for different cells would allow to visualize results while solving.
Temperature Cell 1
1
In the Definitions toolbar, click  Probes and choose Global Variable Probe.
2
In the Settings window for Global Variable Probe, type Temp1 in the Variable name text field.
3
In the Label text field, type Temperature Cell 1.
4
Locate the Expression section. In the Expression text field, type lb.Temp.
5
From the Table and plot unit list, choose degC.
6
Select the Description check box.
7
In the associated text field, type Cell 1.
8
Click to expand the Table and Window Settings section. Click  Add Table.
9
From the Plot window list, choose New window.
10
Click  Add Plot Window.
Temperature Cell 2
1
Right-click Temperature Cell 1 and choose Duplicate.
2
In the Settings window for Global Variable Probe, type Temperature Cell 2 in the Label text field.
3
In the Variable name text field, type Temp2.
4
Locate the Expression section. In the Expression text field, type lb2.Temp.
5
In the Description text field, type Cell 2.
Temperature Cell 3
1
Right-click Temperature Cell 2 and choose Duplicate.
2
In the Settings window for Global Variable Probe, type Temperature Cell 3 in the Label text field.
3
In the Variable name text field, type Temp3.
4
Locate the Expression section. In the Expression text field, type lb3.Temp.
5
In the Description text field, type Cell 3.
Cell Potential 1
1
Right-click Temperature Cell 3 and choose Duplicate.
2
In the Settings window for Global Variable Probe, type Cell Potential 1 in the Label text field.
3
In the Variable name text field, type Ecell1.
4
Locate the Expression section. In the Expression text field, type lb.Ecell.
5
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Lumped Battery>lb.E_cell - Cell potential - V.
6
Locate the Expression section. In the Description text field, type Cell 1.
7
Locate the Table and Window Settings section. Click  Add Table.
8
From the Plot window list, choose New window.
9
Click  Add Plot Window.
Cell Potential 2
1
Right-click Cell Potential 1 and choose Duplicate.
2
In the Settings window for Global Variable Probe, type Cell Potential 2 in the Label text field.
3
In the Variable name text field, type Ecell2.
4
Locate the Expression section. In the Expression text field, type lb2.Ecell.
5
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Lumped Battery 2>lb2.E_cell - Cell potential - V.
6
Locate the Expression section. In the Description text field, type Cell 2.
Cell Potential 3
1
Right-click Cell Potential 2 and choose Duplicate.
2
In the Settings window for Global Variable Probe, type Cell Potential 3 in the Label text field.
3
In the Variable name text field, type Ecell3.
4
Locate the Expression section. In the Expression text field, type lb3.Ecell.
5
Click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Lumped Battery 3>lb3.E_cell - Cell potential - V.
6
Locate the Expression section. In the Description text field, type Cell 3.
Study 1
Step 1: Time Dependent
1
In the Model Builder window, under Study 1 click Step 1: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
From the Time unit list, choose h.
4
In the Output times text field, type 0 0.8/C_rate.
5
In the Model Builder window, click Study 1.
6
In the Settings window for Study, locate the Study Settings section.
7
Clear the Generate default plots check box.
8
In the Home toolbar, click  Compute.
Results
Add a dataset with a selection and mirror it twice in order to visualize the temperature of the full 6s2p configuration.
Study 1/Solution 1 (3) (sol1)
In the Results toolbar, click  More Datasets and choose Solution.
Selection
1
In the Results toolbar, click  Attributes and choose Selection.
2
In the Settings window for Selection, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 1 3-21 in the Selection text field.
6
Click OK.
Mirror 3D 1
1
In the Results toolbar, click  More Datasets and choose Mirror 3D.
2
In the Settings window for Mirror 3D, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (3) (sol1).
4
Locate the Plane Data section. In the X-coordinate text field, type 2.5*(d_batt).
Mirror 3D 2
1
Right-click Mirror 3D 1 and choose Duplicate.
2
In the Settings window for Mirror 3D, locate the Data section.
3
From the Dataset list, choose Mirror 3D 1.
4
Locate the Plane Data section. From the Plane list, choose zx-planes.
5
In the y-coordinate text field, type d_batt/2.
6
Click  Plot.
Study 1
Step 1: Time Dependent
1
In the Model Builder window, click Step 1: Time Dependent.
2
Drag and drop below Step 1: Time Dependent.
Results
Cell Temperatures vs. Time
1
In the Model Builder window, expand the Results>Probe Plot Group 1 node, then click Probe Plot Group 1.
2
In the Settings window for 1D Plot Group, type Cell Temperatures vs. Time in the Label text field.
3
Locate the Plot Settings section. Select the x-axis label check box.
4
Select the y-axis label check box.
5
In the associated text field, type Cell Temperature (degC).
6
Locate the Legend section. From the Position list, choose Lower right.
7
In the Cell Temperatures vs. Time toolbar, click  Plot.
Cell Potential vs. Time
1
In the Model Builder window, under Results click Probe Plot Group 2.
2
In the Settings window for 1D Plot Group, type Cell Potential vs. Time in the Label text field.
3
Locate the Plot Settings section. Select the x-axis label check box.
4
Select the y-axis label check box.
5
In the associated text field, type Cell Potential (V).
6
In the Cell Potential vs. Time toolbar, click  Plot.
Temperature
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Dataset list, choose Mirror 3D 2.
4
In the Label text field, type Temperature.
Surface 1
1
Right-click Temperature and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
From the Unit list, choose degC.
4
In the Temperature toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Appendix — Geometry Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
Click  Done.
Global Definitions
Geometry Parameters
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, type Geometry Parameters in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file lumped_li_battery_pack_6s2p_geom_sequence_parameters.txt.
Geometry 1
Cylinder 1 (cyl1)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type r_batt.
4
In the Height text field, type h_batt.
Cylinder 2 (cyl2)
1
Right-click Cylinder 1 (cyl1) and choose Duplicate.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type r_term.
4
In the Height text field, type h_term.
5
Locate the Position section. In the z text field, type -h_term.
Array 1 (arr1)
1
In the Geometry toolbar, click  Transforms and choose Array.
2
In the Settings window for Array, locate the Input section.
3
Click  Paste Selection.
4
In the Paste Selection dialog box, type cyl2 in the Selection text field.
5
Click OK.
6
In the Settings window for Array, click to collapse the Displacement section.
7
Locate the Size section. In the z size text field, type 2.
8
Click to expand the Displacement section. In the z text field, type h_batt+h_term.
Array 2 (arr2)
1
Right-click Array 1 (arr1) and choose Duplicate.
2
In the Settings window for Array, locate the Input section.
3
Find the Input objects subsection. Click to select the  Activate Selection toggle button.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type cyl1 in the Selection text field.
6
Click OK.
7
In the Settings window for Array, locate the Input section.
8
Click  Paste Selection.
9
In the Paste Selection dialog box, type arr1(1,1,1) in the Selection text field.
10
Click OK.
11
In the Settings window for Array, locate the Input section.
12
Click  Paste Selection.
13
In the Paste Selection dialog box, type arr1(1,1,2) in the Selection text field.
14
Click OK.
15
In the Settings window for Array, locate the Size section.
16
In the x size text field, type 3.
17
Locate the Displacement section. In the x text field, type d_batt.
18
In the z text field, type 0.
19
Click  Build Selected.
Block 1 (blk1)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type d_batt+d_sc.
4
In the Depth text field, type d_sc.
5
In the Height text field, type h_sc.
6
Locate the Position section. In the x text field, type -d_sc/2.
7
In the y text field, type -d_sc/2.
8
In the z text field, type -h_sc-h_term.
9
Click  Build Selected.
Block 2 (blk2)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type (d_batt+d_sc)/2.
4
In the Depth text field, type d_sc.
5
In the Height text field, type h_sc.
6
Locate the Position section. In the x text field, type -d_sc/2+(d_batt)*2.
7
In the y text field, type -d_sc/2.
8
In the z text field, type -h_term-h_sc.
Block 3 (blk3)
1
Right-click Block 2 (blk2) and choose Duplicate.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type (d_batt)/2+d_sc.
4
Locate the Position section. In the x text field, type -d_sc/2-d_batt/2.
5
In the z text field, type h_batt+h_term.
Block 4 (blk4)
1
Right-click Block 3 (blk3) and choose Duplicate.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type w_pc.
4
In the Depth text field, type d_batt/2+w_pc/2.
5
In the Height text field, type h_pc.
6
Locate the Position section. In the x text field, type -w_pc/2.
7
In the y text field, type -w_pc/2.
8
In the z text field, type -h_term-h_sc-h_pc.
9
Click  Build Selected.
Move 1 (mov1)
1
In the Geometry toolbar, click  Transforms and choose Move.
2
Click the  Zoom Extents button in the Graphics toolbar.
3
Click the  Transparency button in the Graphics toolbar.
4
In the Settings window for Move, locate the Input section.
5
Click  Paste Selection.
6
In the Paste Selection dialog box, type blk1 in the Selection text field.
7
Click OK.
8
In the Settings window for Move, locate the Input section.
9
Select the Keep input objects check box.
10
Locate the Displacement section. In the x text field, type d_batt.
11
In the z text field, type h_batt+h_term*2+h_sc.
12
Click the  Zoom Extents button in the Graphics toolbar.
Array 3 (arr3)
1
In the Geometry toolbar, click  Transforms and choose Array.
2
In the Settings window for Array, locate the Input section.
3
Click  Paste Selection.
4
In the Paste Selection dialog box, type blk4 in the Selection text field.
5
Click OK.
6
In the Settings window for Array, locate the Size section.
7
In the x size text field, type 3.
8
In the z size text field, type 2.
9
Locate the Displacement section. In the x text field, type d_batt.
10
In the z text field, type h_batt+2*(h_term+h_sc)+h_pc.
11
Click  Build Selected.
Move 1 (mov1)
1
In the Model Builder window, click Move 1 (mov1).
2
In the Settings window for Move, click  Build Selected.
3
Click  Build All Objects.
Work Plane 1 (wp1)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
In the z-coordinate text field, type -(h_term+h_sc+h_pc).
Work Plane 1 (wp1)>Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 1 (wp1)>Circle 1 (c1)
1
In the Work Plane toolbar, click  Circle.
2
In the Settings window for Circle, locate the Size and Shape section.
3
In the Radius text field, type r_batt.
4
In the Sector angle text field, type 90.
5
Locate the Rotation Angle section. In the Rotation text field, type 180.
Work Plane 1 (wp1)>Square 1 (sq1)
1
In the Work Plane toolbar, click  Square.
2
In the Settings window for Square, locate the Size section.
3
In the Side length text field, type r_batt.
4
Locate the Position section. In the xw text field, type -r_batt.
5
In the yw text field, type -r_batt.
Work Plane 1 (wp1)>Difference 1 (dif1)
1
In the Work Plane toolbar, click  Booleans and Partitions and choose Difference.
2
Click the  Zoom Extents button in the Graphics toolbar.
3
Select the object sq1 only.
4
In the Settings window for Difference, locate the Difference section.
5
Find the Objects to subtract subsection. Click to select the  Activate Selection toggle button.
6
Click  Paste Selection.
7
In the Paste Selection dialog box, type c1 in the Selection text field.
8
Click OK.
9
In the Settings window for Difference, click  Build Selected.
Work Plane 1 (wp1)>Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 3*(d_batt).
4
In the Height text field, type d_batt.
5
Click  Build Selected.
6
Locate the Position section. In the xw text field, type -r_batt.
7
In the yw text field, type -r_batt.
Work Plane 1 (wp1)>Difference 2 (dif2)
1
In the Work Plane toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object r1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Find the Objects to subtract subsection. Click to select the  Activate Selection toggle button.
5
Click the  Zoom Extents button in the Graphics toolbar.
6
Select the object dif1 only.
7
Click  Build Selected.
Extrude 1 (ext1)
1
In the Model Builder window, right-click Geometry 1 and choose Extrude.
2
In the Settings window for Extrude, locate the Distances section.
3
In the table, enter the following settings:
Distances (m)
h_batt+2*(h_term+h_sc+h_pc)
4
Click  Build Selected.
Form Union (fin)
In the Geometry toolbar, click  Build All.
Battery 1
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
On the object fin, select Domain 3 only.
3
In the Settings window for Explicit Selection, type Battery 1 in the Label text field.
Battery 2
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
On the object fin, select Domain 10 only.
3
In the Settings window for Explicit Selection, type Battery 2 in the Label text field.
Battery 3
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
On the object fin, select Domain 16 only.
3
In the Settings window for Explicit Selection, type Battery 3 in the Label text field.
Air Domain
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
On the object fin, select Domain 2 only.
3
In the Settings window for Explicit Selection, type Air Domain in the Label text field.
Connectors
1
In the Geometry toolbar, click  Selections and choose Complement Selection.
2
In the Settings window for Complement Selection, locate the Input Entities section.
3
Click  Add.
4
In the Add dialog box, in the Selections to invert list, choose Battery 1, Battery 2, Battery 3, and Air Domain.
5
Click OK.
6
In the Settings window for Complement Selection, type Connectors in the Label text field.
7
In the Geometry toolbar, click  Build All.
Batteries
1
In the Geometry toolbar, click  Selections and choose Union Selection.
2
In the Settings window for Union Selection, locate the Input Entities section.
3
Click  Add.
4
In the Add dialog box, in the Selections to add list, choose Battery 1, Battery 2, and Battery 3.
5
Click OK.
6
In the Settings window for Union Selection, type Batteries in the Label text field.
Batteries and Connectors
1
In the Geometry toolbar, click  Selections and choose Union Selection.
2
In the Settings window for Union Selection, locate the Input Entities section.
3
Click  Add.
4
In the Add dialog box, in the Selections to add list, choose Connectors and Batteries.
5
Click OK.
6
In the Settings window for Union Selection, type Batteries and Connectors in the Label text field.
Heat Flux Boundaries
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, locate the Entities to Select section.
3
From the Geometric entity level list, choose Boundary.
4
In the Label text field, type Heat Flux Boundaries.
5
Locate the Entities to Select section. Click  Paste Selection.
6
In the Paste Selection dialog box, type fin: 1-7, 9, 12, 14, 15, 48 in the Selection text field.
7
Click OK.
8
Click the  Wireframe Rendering button in the Graphics toolbar.
9
Click the  Zoom Extents button in the Graphics toolbar.
10
In the Geometry toolbar, click  Build All.